If(x-1/X)=5 find the value
(X2+1/X2)
(x4+1/x4)
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Answer:
The value of x² + 1/x² is 27 and the value of
x⁴ + 1/x⁴ is 727.
Given:
(x - 1/x) = 5
To find:
- (x² - 1/x²) and (x⁴ - 1/x⁴)
Solution:
》x - 1/x = 5
On squaring both sides
》x² - 2 (x) (1/x) + 1/x² = 25
》x² + 1/x² = 27
On squaring both sides
》x⁴ + 2 (x²) (1/x²) + 1/x⁴ = 729
》x⁴ + 1/x⁴ = 729 - 2
》x⁴ + 1/x⁴ = 727
Therefore, the value of x² + 1/x² is 27 and the value of x⁴ + 1/x⁴ is 727.
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